and what main organising formulations or
hubs can we find in GS, such as abstraction.

I hope this will help refresh our GS knowledge
and act a a good introduction to GS as a system.

Led by David Hewson.

1.
Catching-up

We “always” allow a little
time for review of our lives and activities.

At this first Seminar Meeting
for 2010, we had plenty of catching-up to do!

2. David’s Presentation - Objective

* To review GS
formulations and get a better understanding of GS as a system.

* To help GS students
organise their knowledge.

3.
GS Formulation Networking

We started with some
exercises to show how communication depends on context. E.g. the
statement "Laurie should run" can be interpreted as about health and
exercise or about AGS politics and who should hold office this year, depending
on the context.
Another exercise showed up how the order we receive ideas in, also affects how
we view them.
(See “Science and Sanity” p444-445 for more on this. DeBono’s book
“Mechanism of Mind” also has some information on this.)

The motivation for the
talk came from a paper titled “A Network Model of Knowledge Acquisition”
They suggest the idea that organisation of knowledge in an individual’s brain
can be considered a network. Network science can suggest how information
can be organized in the brain. A hierarchy of three increasingly sophisticated
network systems -- a random network, a small world network and a scale free
network (to be discussed later) can be used to model the increasing
sophistication of knowledge networks as they evolve during learning.

The aim is to help
students learn effectively, by helping them:
“... understand facts and ideas in a context of a conceptual framework and to
organize their knowledge in ways that facilitate retrieval and application.”

Network science
developed late in the 20th century. It grew out of our need to understand the
structure and dynamics of the many complex networks in mathematics, physics,
sociology, psychology and engineering. One famous general semanticist,
Anatol Rapoport did some research in this area on social networks. One
well known notion of “six degrees of separation” implies that an individual in
a particular population can contact another individual through a directed chain
of, on average, six contacts or less.

A network is a
collection of objects called nodes, connected in pairs, by lines called
links. For example a social network of your friends. You and each of your
friends are nodes connected by links representing friendship. In a
knowledge network the nodes represent formulations and the links
represent relationships between them like: “part of” (e.g. the object
level is part of the structural differential) or “kind of” (e.g.
“fact-inference confusion” is a kind of identification between levels) or
“manner” (e.g. deleting, distorting and generalising are different ways we can
abstract.), etc.

A couple of properties
of networks are:
1) the average number of the links which serves as a measure of
penetration of links into the network. E.g. “six degrees of separation”.
2) the cluster coefficient which measures how tightly the linked nodes are
clustered together. So we have the notion that "a few large nodes
carry most of the connections." The Web, for example, is "dominated
by a few very highly connected nodes, or hubs... such as Google or
Amazon.com.".

Networks of knowledge start
off as random networks with few links and no organisation. They then move
on to small world networks with more links and things begin to cluster. And finally
it ends up as a scale free network, very organised around some main hubs.

So the three sorts of
network are:
1) A random network. This sort of network has nodes with few links and no
overall structure. Imagine someone gives you 20% of a jigsaw puzzle
pieces in a random order. The network you build from this would look like
a random network. It would have mostly unlinked pieces (nodes) with a few
clusters of partially linked pieces.
2) A small-world network is a type of network in which most nodes are not
neighbours of one another (i.e. not linked to each other), but most nodes can
be reached from every other by a small number of links. So a small world
network, where nodes represent people and links show that people that know each
other, captures the small world phenomenon of strangers being linked by at most
6 mutual acquaintances.
3) A scale free network develops out of a small world network when the most
preferred nodes, called hubs, form centres about which most information is
organised. I.e. the knowledge is clustered and organised by these hubs.

So teachers can help
students identify hubs of knowledge and link what they are learning into these
hubs. This will help them form the scale free network of the
sophisticated learner.

We performed an exercise
to see how we organise our GS knowledge. I.e. What links can we make
between formulations and what main organising formulations or hubs can we find
in GS? And here is our result: